Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction

Chechkin, Gregory A.; Chechkina, T. P.; D’Apice, Ciro; Maio, Umberto De; Mel'nyk, Taras A.

doi:10.1134/s1061920810010048

Cited by 8 publications

(18 citation statements)

References 22 publications

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“…In very rough boundaries, the boundary Γ ε can be defined by 2 = ( 1 , 1 ⁄ ), with > 1. For the treatment of randomly defined surface roughness, see [30][31][32][33].…”

Section: Mathematical Bounds On the Effects Of Surface Roughness Usinmentioning

confidence: 99%

A computational study of the influence of surface roughness on material strength

et al. 2018

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In machine component stress analysis, it usually assumed that the geometry specified in CAD provides a fair representation of the geometry of the real component. While in particular circumstances, tolerance information, such as minimum thickness of a highly stressed region, might be taken into consideration, there is no standard practice for the representation of surface quality. It is known that surface roughness significantly influences fatigue life, but for this to be useful in the context of life prediction, there is a need to examine the nature of surface roughness and determine how best to characterise it. Non-smooth geometry can be represented in mathematics by fractals or other methods, but for a representation to have a practical value for a manufactured component, it is necessary to accept that there is a lower limit to surface profile measurement resolution. Resolution and mesh refinement also play a part in any computational analysis undertaken to assess surface profile effects: in the analyses presented, a nominal axi-symmetric geometry has been taken, with a finite non-smooth region on the boundary. Various surface roughness representations are modelled, and the significance of the characterized surface roughness type is investigated. It is shown that the applied load gives rise to a nominally uni-axial stress state of 90% of the yield, although surface roughness features have the effect of modifying the load path, and give rise to localized regions of plasticity near to the surface. The material of the test model is assumed to be elasto-plastic, and the development and evolution of plastic zones formed within the geometry are shown for multiple load cycles.

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“…In very rough boundaries, the boundary Γ ε can be defined by 2 = ( 1 , 1 ⁄ ), with > 1. For the treatment of randomly defined surface roughness, see [30][31][32][33].…”

Section: Mathematical Bounds On the Effects Of Surface Roughness Usinmentioning

confidence: 99%

A computational study of the influence of surface roughness on material strength

et al. 2018

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“…To study such phenomenon we apply the homogenization methods (cf., for example, [44,8,4,49,38,45,14]). These methods enable to explore media with periodic or quasiperiodic microstructure as well as with random one (see, for instance, [15,16,17,1,18,19]).…”

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confidence: 99%

“…The functions g j model inhomogeneous external actions and can be interpreted as flux of light, radiation, etc. Note that the complex Ginzburg-Landau equation can also be written in the form (17) (see [28,53]).…”

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confidence: 99%

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Strong convergence of trajectory attractors for reaction–diffusion systems with random rapidly oscillating terms

Bekmaganbetov¹,

Chechkin²,

Chepyzhov

2020

Communications on Pure &Amp; Applied Analysis

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We consider reaction-diffusion systems with random terms that oscillate rapidly in space variables. Under the assumption that the random functions are ergodic and statistically homogeneous we prove that the random trajectory attractors of these systems tend to the deterministic trajectory attractors of the averaged reaction-diffusion system whose terms are the average of the corresponding terms of the original system. Special attention is given to the case when the convergence of random trajectory attractors holds in the strong topology.

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“…We refer here to homogenization methods (cf., for example, [4,7,14,38,42,45]), which are basic for studying mathematical problems in micro-nonhomogeneous media. These methods enable to consider media with periodic microstructure as well as with random one (for random case cf., for instance, [1,15,16,17,18,19]).…”

mentioning

confidence: 99%

Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms

Chechkin¹,

Chepyzhov²,

Pankratov³

2018

Discrete &Amp; Continuous Dynamical Systems - B

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We consider complex Ginzburg-Landau (GL) type equations of the form: ∂tu = (1 + αi)∆u + R u + (1 + βi) |u| 2 u + g, where R, β, and g are random rapidly oscillating real functions. Assuming that the random functions are ergodic and statistically homogeneous in space variables, we prove that the trajectory attractors of these systems tend to the trajectory attractors of the homogenized equations whose terms are the average of the corresponding terms of the initial systems.

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Homogenization of 3D thick cascade junction with a random transmission zone periodic in one direction

Cited by 8 publications

References 22 publications

A computational study of the influence of surface roughness on material strength

A computational study of the influence of surface roughness on material strength

Strong convergence of trajectory attractors for reaction–diffusion systems with random rapidly oscillating terms

Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms

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